Irreversibly dischargeable photographic filter layers and method of processing film containing the same



United States Patent Ofiice IRREVERSIBLY DISCHARGEABLE PHOTO- GRAPHICFILTER LAYERS AND METHOD 0F' PROCESSING FILM CONTAINING THE SAME"sevolod Tula'gin, Phillipsbnig, N. J., assignor to General Aniline &Film Corporation, New York, N. Y., a corporation of Delaware ApplicationDecember 9, 1950, Serial No. 200,095

7 Claims. (Cl. 952) lhe present invention relates to irreversiblydischargeable photographic tilter and antihalation layers containing asthe active filtering agent, a yellow non-diffusing Schifs base, and to amethod of processing photographic material containing the same.

Multi-layer color film, as commercially exploited at the present time,is constructed in the form of an integral tri-pack comprising a base andthree superimposed silver halide emulsion layers thereon, sensitized,respectively, in the order of their arrangement on the base to red,green and blue light.

lt is known that all high-speed photographic emulsions` are highlysensitive to blue light. Consequently, in the present-day colormaterial, there is always present bctween the blue and green sensitivelayers, filter layer. This filter layer contains a yellow colorant whichabsorbs blue light, thus preventing it from reaching and exposing thegreen and red sensitive layers.

The yellow colorant. in order to be effective in the intendedrelationship, inust possess certain prerequisites. Thus, it must becapable of being completely removed during the processing of the film.`Unless it be so re.- moved, the whole material would be colored yellowand the formation of white or transparent areas would be impossible.

The colorant must also be non-migratory in the colloid employed as thecarrier therefor. If the colorant should migrate from the filter layer,to adjacent silver halide emulsion layers, it would seriously interferewith the spectral sensitivities thereof. Color degradation wouldinevitably ensue.

The colorant must be a "brilliant" one; that is to say, the colorantshould absorb a large percentage of the blue light and yet be almostcompletely transparent to the green and red regions of the spectrum.fest that unless the colorant is capable of this operation, its purposecannot be completely attained.

Finally, the colorant must be either water soluble or dispersible in anaqueous solution of the colloid serving as a carrier therefor.

possess many of the characteristics of an excellent filter 7 dye, theysutler from the disadvantage that they are migratory in the watersoluble colloidal material serving as a basc for the filter layer. Thus,it is evident that the provision of a satisfactory yellow colorant forfilter or antihaliition layers is not the simple problem that it might,at first blush, appear to be.

lt is mani- 5.

Patently, without this property, the difiiculties of manufacturing thefilter layer would 2,695,233 Patented Nov. 23, 1954 l have nowdiscovered that minus blue colorants, having all of the necessaryprerequisites, are those which are obtained by the condensation of orthohydroxy aldehydcs with primary aliphatic or aromatic amines, either thcaldehyde or the amine being provided with a group which renders thecondensation product non-migratory in colloidal materials.

Filter layers (it being understood that this term iiicludesanti-halation layers) containing such yellow colorants, and a method ofprocessing photographic materials containing such filter orantilialation layers to effect the discharge of the colorantsirreversibly, constitute the purposes and objects of the presentinvention.

The yellow colorants, the utilization of which is contemplated herein,may be characterized by the following structural formulae:

fi'za iii which X is hydrogen, alkyl such as methyl, ethyll, propyl,butyl or the like, hydroxyalkyl such as hydroxymethyl, hydroxyethyl orthe like, aryl such as phenyl', toluyl or the like, nitro, hydroxy,sulfo. carboxy, acylamino such as acetylaniino, butrylamino,lauroylamino, stearoylamino or the like, amino, alkylamino such asmethylamino, ethylarnino, butylainino, decylamino, dodecylamino,octadecylaniino, diniethylamino, diethylamino, dibutylamino or the like,cyaiio and acyloxyalkyl such as carboxymethyl or the like, Z representsthe atoms necessary to complete a -inembered aromatic or heterocyclicring containing a conjugated, unsaturated system such as benzo, pyridoand the like and A is aliphatic such as methyl, ethyl, butyl, cetyl,decyl, dodecyl, octadecyl, or the like, or aromatic such as phenyl,toluyl, dimethylphenyl, sulfoplienyl, tetradecoxyphenyl, dodecoxyphenyl,p-sulfododecoxyphenyl, lauroylaminophenyl, psulfooctadecylsulfonamidophenyl, ni sulfostearoylaminotoluyl,p-sulfooctadecylaminophenyl, (1octadecyl 5'-sulfobenzimidazolyl)phenyl,and the like.

It is evident that certain of the above substituent groups, such ashydroxyamino or substituted amino, are auxochromes. By the utilizationof such substituents, the color of the yellow dyes may be varied. Thisis important since it enables the production of yellow filter dyes witha wide range of different spectral adsorptions.

A number of the substituents mentioned are also negative in character,and in this group may be mentioned the nitro, sulfo, carboxy and cyanogroups. Such groups have the ability to stabilize the dyestutis tooxidation and hydrolysis.

Ithas been stated that the ease of dissolving or dispersing thecolorants in aqueous colloidal solutions is a desirable feature of theyellow filter dyes. This property is often attributable to theutilization, as substituents, of groups mentioned above, having a watersolubilizing function such as the sulfo, carboxy, hydroxy andhydroxyalkyl groups.

ln the above compounds, the hydroxyl group is always in ortho positionto'the azomethine linkage. lt has been found that the oxygen of thishydroxyl group is enolic in character since the hydrogen bound theretois labile. This has been indicated in the above formulae by the dottedlines running from the hydroxyl group to the nitrogen atom of theazomethine linkage.

and

Examples of compounds embraced by the above formulae which I have foundanswer the above prerequisites are the following.

(1) (I'JiBu N\ Hons N HO

(2) (llnHu /N\ (l)E nois- N CU (3) CHA CiIHssC CHN- N CH C17Hx5COHN-N=CH SIOxH COOH (5) (IMHU N\ 1 C@ Hois N H0 COOH () (IlllH N\ CH:

Hofs

N HO

(7) (IJH=NCH| CnHIsCOHN BOIH (s) N CH l 0H CuHza Hx I SOIH 0H HOllIHSOnCuHn fil (10) N CH CH: HO-

i NHCO CnHas (u) Ci2Hz5N=CH SOaH (i2) CH: 110

H035- NHCO OUH l N02 (13) TTT-CH -O CnHzs \OH HOS HO O C l (14) N=CH IOH H03S NH-'CizHzs The above compounds are prepared by heating an orthohydroxy aldehyde with a primary aliphatic or aromatic amine. Either theamine or the aldehyde must contain a radical which renders the dyestuffmolecule non-diffusing in a colloidal medium. This end is preferablyachieved by incorporating in either the aldehyde or the primary amine,an alkyl chain of at least 10 carbon atoms.

The aldehydes which are employed have the following structural formulae:

CHO

in which X and Z have the values given above, and the hydroxyl group isalways in ortho position to the aldehydic group.

Examples of aldehydes which I have found to be eminently suitable forthe production of the Schiffs bases are and XXXII.2-hydroxy--stearoylamino-naphthaldehyde-4-sulfonic acid XXXIII.2-hydroxy-naphthaldehyde--carboxylic acid XXXIV.2-hydroxy-6-amino-naphthaldehyde XXXV.2-hydroxy-4-octadecylamino-naphthaldehyde XXXVI.2-formyl-3-hydroxyquinoline of the following structure:

N ono f XXXVII. 3-formyl-4-hydroxyquinaldine of the following structure:

HaC-

OHG

l oH XXXIII. 3-acetoxymethyl-S-methyl-Z-hydroxybenzaldehy e The amineswhich are employed may be aliphatic or aromatic mono-primary amines.Examples of aliphatic amines are methyl amine, ethyl amine, butyl amine,cetyl amine, decyl amine, dodecyl amine, octadecyl amine, or the like.

Examples of aromatic amines are aniline, o-, m, or ptoludine, o, m, orp-xylidine, the mono-primary amines disclosed in copending applicationSerial No. 43,756 filed by Joseph A. Sprung on August ll, 1948, nowPatent No. 2,629,658, entitled Silver Halide Emulsions ContainingNon-Ditlusing Azo Dyes such as 2-tetrodecoxy-aniline4-tetradecoxy-aniline 2-dodecoxy-aniline-5-sulfonic acid2-oetadecoxy-aniline-S-sulfonic acid 4-amino-lauranilide5-octadecane-sulfonamido-orthanilic acid 4-methyl-S-Stearamido-metanilicacid, and the like,

4-methylamino-6-stearoylamino-metanilic acid of the formula CnHaiC OHN-NH:

4-octadecylamino-metanilic acid fonic acid, of the formula INI-*0151131Practically all of the aldehydes previously referred to are described inthe literature. Those which are not so described may be made byrelatively simple procedures. Thus,Z-hydroxy--stearoylamino-naphthaldehyde is prepared by reducing2-hydroxy-6-nitro-naphthaldehyde with an alkyline hydrosullite solution,followed by a treatment of the cooled reduction mixture withstearoylchloride. The sultonie acid derivative of this aldehyde isobtained by sull'onating the same with concentrated sulfuric acid at 50to 60 C. for several hours.

l-formyl-2-hydroxynaphthalene--carboxylic acid is made by theapplication of the Reimer-Tiemann reaction to 6-hydroxy-2-naphthoicacid. For a denition of the Reimer-Tiemann reaction, reference is madeto page of Organic Chemistry by Gilman, vol. l, Second Edition.

2-hydroxy-3-cyano-benzaldehyde is prepared by diazotizing2hydroxy3amino-benzaldehyde and reacting the resulting diazoniumcompound with cuprous cyanide according to the Sandmeyer reaction.

3acetoxymethyl5-methyl 2 hydroxybenzaldehyde is prepared by retluxing3-chloromethyl-S-methyl-Z-hydroxybenzaldehyde (Berichte 63B, 55-19) withsodium acetate in ethyl alcohol.

The last three amines mentioned above, and having long aliphatic chains,are described in Fiat Final Report #943.

The above colorants may be solubilized for dispersion in a colloidalcarrier by various methods. Thus the dyes may be suspended in absolutealcohol and enough alkali, such as sodium hydroxide, added to obtain aneutral solution. Water is then added until a uniform solution ensues.

Conversely, the dye may be suspended in alcohol. and a base, such asmorpholine, is cautiously added until the dye is brought into solution.Water is then incorporated, and the mixture stirred until it ishomogeneous.

Solutions of the dye, produced as above, are incorporated into'anaqueous colloidal carrier such as gelatin, polyvinyl alcohol, thecopolymer of maleic anhydride and methylvinyl ether by adding to asolution of the dyestuif, slowly and with agitation, a 10% aqueoussolution of the colloid selected. lf a base such as morpholinc has beenemployed for solubilization of the dyestuli, the solution of the colloidis adjusted to a pH of 7 to 8 by the addition of sodium hydroxide priorto mixing it with the dye solution. The mixture attained in this way isstored until homogeneous and then used in the coating of photographicfilm.

It has been ascertained, and this constitutes a very important featureof my invention, that lter or antihalation layers containing thecolorants of the present invention may be completely and irreversiblydischarged by the use ot a bath containing a base such as hydrazine,hydroxylamine or a semi-carbazide such as semi-carbizide itself or thosedescribed kin United States Letters Patent 2,495,000 granted .Ianuaryl7, l950, or the salts of such bases, such as the hydrochloride,sulfate, phosphate, formate, nitrate and the like, i. e. hydroxylamine,hydrochloride, hydroxylamine sulfate, hydrazine hydrochloride, hydrazineformate, liydrazine nitrate. hydrazine sulfate and the salts of thesemi-carbazides described in the aforementioned USP 2.495,000. Whilethese solutions operate on the alkaline side, and indeed at almost anypH, best results ensue when the solutions are buffered to the acid side,i. e. within a range of pH 6 to 2. In using the solutions, it isrecommended that they be employed at a temperature ranging from about 65to 70 F.

In the event that the filter layer appears in multilayer color lm, thenthe discharging bath may be substituted for one of the acid short-stopbaths used in color film processing. When employed in this way, thesolutions do not add any extra step or complicate the usual processing.lt is, of course, evident that the solutions may be employed asindependent processing baths, either in the working up of color lm or ofblack and white lrn when the colorants hereof are used as antihalationor filter layers in such black and white film.

The following examples serve to illustrate the invention, but it is tobe understood that the invention is not restricted thereto. The partsare by weight, unless otherwise stated.

SECTION I Preparation of dyes EXAMPLE 1 Into a 500 cc. flask equippedwith a short fraclionating column and an agitator, are placed 40.5 g.(.075 mole) of the amine, 2(4'aminophenyl)-l-octadccylbemzimidazole-S-sulfonic acid, 250 cc, of glacial acetic acid and cc. ofpyridine. Z-hydroxy-l-naphthaldehyde (26 g.=.15 mole) was added and themixture was siowly refiuxed under the column. The water was thusdistilled out as it formed. After 4 hours 30 cc. of distillate had beenobtained and the mixture was deeply colored. The hot solution wasfiltered and the filtrate was cooled. The crystalline material wascollected by filtration, washed with alcohol and crystallized fromdimethyl forman'aide. The solid was collected by filtration. thoroughlywashed with absolute alcohol and ether and dried The prod-4 uctconsisted of brilliant orange yellow crystals. A yield of 30 g. wasobtained.

The product corresponds to compound l above.

EXAMPLE ..l

Into a 500 cc. flask equipped with a short fractionating column and anagitator are placed 24 g. of the amine of Example l, 150 cc.'of glacialacetic acid, 30 cc. of pyridine and 8.3 g. of3-formyl-Ll-hydroXy-quinaldine. The mixture is refluxed with slowdistillation for 31/2 hours and then under total redux for 20 hours. Asmall amount of an insoluble impurity was removed by filtration of thehot solution and the filtrate was cooled. The precipitated, whitecrystalline material was removed by filtration and the filtrate wasdiluted with a large volume of acetone. The yellow filter dye whichprecipitated was collected by filtration, washed with acetone und dried.lt was suitable for use without further purilication.

The product corresponds to compound 2 above.

EXAMPLE 3 lnto a i000 cc. round4 bottomed flask equipped with a reliuxcondenser are placed, 47 g. of 4-methylamino- 6-stearoylaminometanilicacid, 17.5 g. of 2-hydroxy-lnaphthaldehyde, 470 cc. of glacial aceticacid and g. of anhydrous sodium acetate and the mixture is refiuxed witha slow distillation of acetic acid for 4 hours. The resulting darksolution is cooled and the `precipitated crystalline yellow dye iscollected by filtration. The solid so obtained is thoroughly extractedwith acetone and dried. The material is suitable for use without furtherpurification.

The product corresponds to compound 3 above.

EXAMPLE t The procedure is the same as in Example 3. excepting that thealdehyde used is 2-hydroxy1-naphthaldehyde- @carboxylic acid.

The product corresponds to compound 4 above.

EXAMPLE 5 The procedure is the same as in Example El, while utilizing asthe amine that of Example l, and while uttllzlng as the aldehyde that ofExample 4.

The product corresponds to compound 5 above.

EXAMPLE (i The procedure is the same as in Example 3 but while using2-hydroxy-S-methylbenzaldehyde as the aldehyde.

The product corresponds to compound 6 above.

EXAMPLE 7 into a 250 cc. round bottomed liask are placed 3 grams of 2hydroxy 6 stearoylamino naphthaldt-.hyde x-i sulfonic acid, 100 cc. ofglacial acetic acid and l cc. ot 30% methyl amine solution. The mixtureis slowly disfilled, through a simple fractionating column for 4 hours.he residual liquid is evaporated on a steam-cone at 22 mm. pressure. Theresidue is thoroughly extracted with a little acetone. The insolubleyellow dye is collected by filtration, washed with acetone, dried andused without further purification.

The product corresponds to that of compound 7 above.

SECTION ll Preparation of dye solutions and filter layers EXAMPLE 600mg. ot the dye ot Example l were suspended in 6 cc. of absolute alcoholand sufficient sodium hydroxide solution was added to obtain a neutralsolution or an alkaline suspension, 40 cc. of water was then added and auniform solution was obtained.

To the above solution was added slowly and with agitation, 20 cc. of 10%aqueous gelatin solution. The mixtare was maintained at 40 C. until usedfor coating, which is effected as promptly as possible.

EXAMPLE 9 l g. of the dye of Example 2 is suspended 1n 6 cc. of alcoholand morpholine is cautiously added until the dye goes into solution. Atthis point the solution should show a pH of 5 to 6 when diluted withwater. 50 cc. of water are added and the mixture is stirred untilhornogeneous.

The above solution is added to l0 ce. of 10% aqueous gelatin solutionwhich has been previously brought to a pl-l of 7 to 8 by the addition ofsodium hydroxide. The mixture is stirred until homogeneous and is thenused in the coating of photographic light sensitive elements.

SECTION III Bleue/zing and short-stop solutions EXAMPLE 1U The followingsolution serves as a combined yellow filter dye beach and short-stopsolution:

Water cc 500 I-iydroxylamine hydrochloride grarns 9 dissolve-then addSodium hydroxide do 4 Water to make 1000 ce.

Bleach for 2 to 5 minutes at 65-70" F.

EXAMPLE 11 Bleaching solution and short-stop both comprised of thefollowing:

Water cc 500 Hydroxylamine hydrochloride grams 35 Sodium acetate(anhydrous) do Water to make 1000 cc.

The following solution serves as a combined yellow filter dye bleach andshort-stop solution:

Water cc-- 500 Hydrazine hydrochloride grams l0 6 N ysodium hydroxide topH 5 Water to make 1000 cc.

SECTION IV Preparation of multi-layer film EXAMPLE 14 A red sensitizedsilver bromide emulsion containing a phenolic color former fast todiffusion is cast upon a base and over this is cast a green sensitivesilver bromide emulsion containing a pyrazolone color former fast todilusion. Over the green sensitive layer is cast a filter layer preparedaccording to Example 8. Over the filter layer 1s cast a blue sensitiveemulsion containing an acetoacetanihde color former fast to diffusion.

EXAMPLE 15 The procedure is the same as in Example 14, excepting thatthe filter layer is prepared according to Example 9.

SECTlON V Film processing EXAMPLE 1o EXAMPLE 17 The procedure is thesame as in Example 16 excepting that the bleach bath of Example l isused as a shortstop bath following the color development with thepdiethylaminoaniline developer.

A photographie material prepared according to Example 17 is exposed anddeveloped in a color developer of the p-diethylaminoaniline type.Following color development, the film is short-stopped in the bath ofExample 12, washed, bleached and fixed.

In the accompanying drawing, the two figures are enlarged section viewsof photographic elements having filter layers and antihalation layersmade according to the present invention. As shown therein, Figure 1illustrates a photographic element comprising a support l having on oneside thereof, a gelatin antihalation layer 2 containing ahydroxy-substituted Schifs base and on the other side, a light sensitivesilver halide emulsion layer 3.

Figure 2 illustrates a multilayer' photographic element having a support4, a red sensitive silver halide emulsion 5, a green sensitive silverhalide emulsion 6 and a blue sensitive silver halide emulsion 8. Betweenlayers 6 and 8, there is coated a gelatin filter layer 7 containing ahydroxy-substituted Schifs base.

Modifications of the invention will occur to persons skilled in the art.Thus it is evident that any of the aldehydes mentioned above may becombined with any of the amines, to form satisfactory yellow colorantsfor filter or antihalation layers. Similarly, while the examples aredirected to the use of the colorants in forming filters for colorphotography, it is understood that the colorants may also be used toform filters and antihalation layers for black and white photography.

I, therefore, do not intend to be limited in the patent granted, exceptas required by the appended claims.

I claim:

l. In the processing of multi-layer photographic color materialcontaining three light sensitive silver halide emulsion layerssensitized respectively to the red, green and blue regions of thespectrum and containing as a yellow filter layer a water soluble colloidhaving dispersed therein a dyestuf selected from the class consisting ofthose of the following formulae:

wherein the hydroxyl group is always ortho to the azo methine linkage,and in which X is a member selected from the class consisting ofhydrogen, alkyl, hydroxyalkyl, aryl, amino, acylamino, acyloxyalkyl,hydroxy,

nitro, sulfo, carboxy and cyano, Z represents the atolrfis necessary tocomplete a -membcrcdring selected from the classl consisting of aromaticand hctcrocyclic rings containing a conjugated unsaturated system and Ais selected from the class consisting of' aliphatic and aromaticradicals involving the exposure of such material and the colordevelopment of the same, the improvement which .comprises dischargingsaid yellow filter dye by subjecting the material to the action of anaqueous bath containing a substance selected from the class consistingof hydroxylamine, hydrazinc and a semi-carbazide and the salts thereof.

2. A light sensitive photographic element comprising a base and lightsensitive silver halide emulsion layer and including as a filter, awater soluble colloid having dispersed therein an irreversiblydischargeable Schilis base selected from the class consisting of thoseof the following formula:

wherein the hydroxyl group is always ortho to the azomethine linkage,and in which X is a member selected from the class consisting'ofhydrogen, alkyl, hydroxyalkyl, aryl, amino, acylamino, acyloxyalkyl,hydroxy, nitro, sulfo, carboxy and cyano, Z represents the atomsnecessary to complete a -memberecl ring selected from the classconsisting of aromatic and heterocyclic rings containing a conjugatedunsaturated system, and A is selected from the class consisting ofaliphatic and aromatic radicals, said Schifis bese containing a groupwhich renders it non-migratory in said water soluble colloid.

3. The light sensitive photographic element defined in clzlaim 2,wherein the filter dye has the following formu a:

CjsHat 4. A light sensitive element as defined in claim 2 wherein saidgroup which renders the Schifis base nonmigratory in the water solublecolloid is an alkyl chain of at least ten carbon atoms.

5. In a multi-layer photographic material containing three lightsensitive silver halide emulsion layers sensitized respectively for thered, green and blue regions of the spectrum, a yellow filter layerinterpolated between the green and blue sensitive emulsion layers,comprising gelatin having dispersed therein, a yellow dyestufi having agroup which renders said dyestufl' non-migratory in gelatin and selectedfrom the class consisting of those of the following formula:

wherein the hydroxyl group is always ortho to the azomethine linkage,and in which X is a member selected from the class consisting ofhydrogen, alkyl, hydroxyalkyl, aryl, amino, acylamino, acyloxyalkyl,hydroxy, nitro, sulfo, carboxy and cyano, Z represents the atomsnecessary to complete a -membered ring selected from the classconsisting of aromatic and heterocyclic rings con` taining a conjugatedunsaturated system and A is selected from the class consisting ofaliphatic and aromatic radicals.

6. The multilayer photographic material as defined in claim 5 whereinthe yellow dyestuli contains a long aliphatic chain which renders thedyestul non-migratory in the gelatin in which it is dispersed.

7. In the processing of a photographic clement comprising a base and alight sensitive silver halide emulsion l 1 layer and including as alter, a water soluble colloid having dispersed therein an irreversiblydischargeable Schiffs base selected from the class consisting of thoseof the following formulae:

and

wherein the hydroxyl group is always ortho to the azomethine linkage,and in which X is a member selected from the class consisting ofhydrogen, alkyl, hydroxyalkyl, aryl, amino, acylamino, acyloxyalkyl,hydroxy, nitro, sulfo, carboxy and cyano, Z represents the atomsnecessary to complete a -rnembered ring selected from the classconsisting of aromatic and heterocyclic rings containing a conjugatedunsaturated system and A is selected from the class consisting ofaliphatic and aromatic radicals, said Schitfs base containing a groupwhich renders it non-migratory in said water soluble colloid, saidprocessing involving the exposure of such material and the developmentof the same, the improvement which comprises irreversbly dischargingsaid Schif's base by subjecting the photographie element to the actionof an aqueous bath containing n substance selected from the classconsisting of hydroxylamine, hydrazine and a semi-carbazide and thesalts thereof.

References Cited in the file of this patent UNITED STATES PATENTS NumberName Date 2,078,398 Mannes et al. Apr. 27, 1937 2,143,786 Mannes et al.Ian.'l0, 1939 2,186,849 Wilmanns et al. Ian. 9, 1940 2,388,903 Cantrellet al Nov. 13, 1945 2,440,070 Bloul et al Apr. 20, 1948 FOREIGN PATENTSNumber Country Date 529,440 Great Britain Nov. 2l, 1940 894,181 FranceMar. 6, 1944 622,731 Great Britain May 6. 1949

1. IN THE PROCESSING OF MULTI-LAYER PHOTOGRAPHIC COLOR MATERIALCONTAINING THREE LIGHT SENSITIVE SILVER HALIDE EMULSION LAYERSSENSITIZED RESPECTIVELY TO THE RED, GREEN AND BLUE REGIONS OF THESPECTRUM AND CONTAINING AS A YELLOW FILTER A WATER SOLUBLE COLLOIDHAVING DISPERSED THERIEN A DYESTUFF SELECTED FROM THE CLASS CONSISTINGOF THOSE OF THE FOLLOWING FORMULAE: